Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:


import java.util.*;
import java.io.*;

public class Main {


    public static void main(String[] args) throws Exception {
        int n = in.nextInt();
        StringBuilder out = new StringBuilder();

        int min = 1;
        int max = n;

        int diff = max - min;
        int m = (int) Math.ceil(diff / 2.0) + 1;

        Pair basePair = new Pair(1, 1);

        out.append(m).append("\n");

        for (int i = 1; i <= n; i++) {
            if (constraint(i, basePair.r, basePair.c)) {
                out.append(new Pair(basePair.r, basePair.c)).append("\n");
            } else {
                i--;
            }
            increment(basePair, m);
        }
        System.out.print(out);
    }

    private static void increment(Pair basePair, int m) {
        if (basePair.c < m) {
            basePair.c++;
        } else {
            basePair.r++;
            basePair.c = 1;
        }
    }

    public static boolean constraint(int i, int ri, int ci) {
        return (ri - 1 + ci - 1) >= (i - 1);
    }

    public static class Pair {
        int r;
        int c;

        public Pair(int r, int c) {
            this.r = r;
            this.c = c;
        }

        @Override
        public String toString() {
            return r + " " + c;
        }
    }


    static class in {

        private static BufferedReader reader;
        private static StringTokenizer tokenizer;

        static {
            reader = new BufferedReader(
                    new InputStreamReader(System.in));
            tokenizer = new StringTokenizer(" ");
        }

        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer(" ");
        }

        static String nextLine() throws IOException {
            return reader.readLine();
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static boolean hasNext() {
            return tokenizer.hasMoreTokens();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static int nextShort() throws IOException {
            return Short.parseShort(next());
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

}